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The evolution of perturbations of renormalized long wave equation. (English) Zbl 0695.35175

Summary: The evolution of the solitary wave solution of the perturbed renormalized long wave equation \(u_ t+6uu_ x-u_{xxt}=\epsilon u\) is considered using two timing and matched asymptotic expansions. As in the case of the perturbed KdV equation, it is found that behind the slowly varying solitary wave there are two distinct regions, a near tail and a far tail. The far tail is given by an exponentially decaying expression in contrast to the KdV far tail which is ocillatory.

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
35C20 Asymptotic expansions of solutions to PDEs
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References:

[1] DOI: 10.1088/0031-8949/20/3-4/023 · Zbl 1063.35531
[2] DOI: 10.1098/rspa.1979.0135 · Zbl 0414.76017
[3] DOI: 10.1017/S0022112073000492 · Zbl 0273.76012
[4] DOI: 10.1098/rsta.1972.0032 · Zbl 0229.35013
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